I test preference and survival rate of one population (moth larvae). I have six varieties of plants (a-f) in six replicates (36 in total) arranged in Latin square block. I applied 5 larvae (1st instar) on each plant (180 larvae applied in total). Plants were isolated from each other by placing them in a mesh sleeve. From the observation my survival data are not normally distributed.
Preference is induced and will be based on the performance (pupa weight, adult weight, eggs laid).
From the visual observation data are not normally distributed.
Do I need to make sure my data is normally distributed (survival across the whole block), e.g. running Shapiro–Wilk test, before considering using ANOVA or use another nonparametric test?
Although ANOVA can be robust against the normality assumption, I would check normality and heterogeneity of data before proceeding with ANOVA or non-parametric test, to justify the test choice. Best of luck!
This is a perennial question, so you can refer to previous discussions, e.g. https://www.researchgate.net/post/I_am_planing_to_do_ANOVA_test_on_my_data_but_the_data_are_not_normally_distributed_even_after_transformation_eg_log_Box-Cox_What_should_I_do
Long story short, ANOVA does not require the data to be normally distributed (ANOVA is just a special case of the general linear model, and the general linear model does not assume that particular variables are normally distributed, only that the residuals are normally distributed), and in any case this assumption about normality is one of the least important (see e.g. https://statmodeling.stat.columbia.edu/2013/08/04/19470/).
BTW It is not a personal question. If you don't have an approximately appropriate sampling distribution your probability statements will be inaccurate. Further the statements on robustness of t and F are often the product of wishful thinking. Be Aware. Best wishes, David Booth
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